Hey guys welcome to another math A lesson today we're going to talk about
compound interest hopefully you would have already seen the simple interest
videos or you already know what simple interest means otherwise it'll be quite
difficult for you to watch the compound interest video and understand what it
means if you're not sure what simple interest is okay so let's have a look at
the definition for compound interest compound interest the principal on which
interest is calculated is increased by adding the interest at the end of each
time period onto the principal so you probably still have no idea what it
means so I'm just going to give you an example and show you by example what
compound interest is so let's have a look at this example
Josh has three thousand dollars to save in the bank he saves this money at eight
percent per annum interest for three years with interest compounded annually
calculate the future value of this investment so basically we want to
calculate how much interest Josh will earn during the three years time and
added on to his principal so the way this is done is going to be quite
different to simple interest so I'll just do a quick reminder of how to do it
if this was simple interest and then I'll show you what compound interest is
so let's pretend so let's have two columns here let's do this problem as if
it was simple interest and let's do this problem
as if it was compound interests
now if you remember simple interest basically all you have to do is find out
what 8% of $3,000 is so three thousand times eight over a hundred is 240
two hundred and forty dollars and simple interests means that every year the
interest is the same is calculated from the principle so two hundred and forty
dollars interest per year now he saves the money for three years so two hundred
and forty times three is seven hundred and twenty and then so that's interest
for three years
and the future value of his investment so the final amount he will receive at the
end is the principal plus the interest which is three thousand plus seven
hundred and twenty which is three thousand seven hundred and twenty so
that's simple interest simple interest is when every year the interest is
calculated from the principal whole at the beginning and for three years
this person has earned seven hundred and twenty dollars added on to the principal
at the beginning which is 3000 plus 720 is three thousand seven hundred and
twenty now let's do this problem for real so we are going to take into
account that this is compound interest so what that means is we're going to
look at this one year at a time so at the end of first year end of first year
the interest that Josh earns at the end of the first year will be three thousand
times 8 out of 100 which is two hundred and forty dollars now here is what here
is the difference if you have a look at our definition from before the principal
is increased by adding the interest at the end of each time period
onto the principal so this is the interest at the end of the first time
period at the end of the first year so we're going to add it on to the
principal so three thousand plus 240 which is three thousand two hundred and
forty now that is the new principal so at the end of the second year what
happens is when we calculate the eight percent interest
we're going to use 3,240 which is our new principal and find 8 percent of that
so three thousand two hundred and forty times eight percent and that's two
hundred and fifty nine point two and then so our principal was 3,240 add the
new interest which is two hundred and fifty nine point two and we get three
thousand four hundred and ninety nine point two
okay and then we have one more year so end of the third year
okay so at the end of the second year our principal was $3499.2
find eight percent of that and then add it on so three four nine nine
point two times eight out of a hundred is two seven nine point nine three and
so our final amount which is the future value is three four nine nine point two
plus two seven nine point nine three
which is three seven seven nine point one four
okay so now we have done this question from both the simple interest
perspective and the compound interest perspective now notice how under the
same conditions with simple interests the future value the final amount is
three thousand seven hundred and twenty whereas under compound interest we have
three thousand seven hundred and seventy nine so that means if you're going to
invest money and the interest rate is the same you want to invest under a
compound interest arrangement because the interest keeps adding on to the
principal and at the end you get a bigger principal and you can also see
that the interest every year is increasing as a result of adding
increasing the principal so the interest in the first year was two hundred and
forty interest in the second year is two hundred and fifty nine interest in the
third year so every year the interest is increasing so that's a good thing when
you are saving money of course when you are earning this money okay so now I'm
going to introduce to you the compound interest formula which will make all of
this a lot easier so the compound interest formula so here is the compound
interest formula and it might look a little bit complicated right now but
that you will get used to it and it gets easier once you have done a few
questions so firstly the A is the final amount or you can say future value
of your investment
R is the rate of interest per annum and n is a new one right n wasn't in our
simple interest formula so n is the variable that we use to state the number
of compounding periods per year number of compounding periods per year so what
does that mean well you can see that here it says interest is compounded
annually so what that means is every year the interest is only added on to
the principal once so n would be one but for example if it said interest
compounded half yearly then n would be two because interest is added on twice a
year or if it said interest compounded monthly then n would be 12 and so on T
is the number of years so then using our P is the principal obviously so using a
formula sorry using these variables let's put in the values for these
variables so the rate of interest is 8% I stated by this number here the number
of compounding periods per year is
one because it says compounded annually so that's one number of years so that
would be three and the principal is three thousand so three thousand so
putting that into the equation we have three thousand
brackets 1 plus the rate is 8%
oops
eight over a hundred times n n is one bracket 1 times T is 3 so
putting all that into the formula now when I type this in I like to
simplify it first before I type it in so 3,000 times I like to work out what's in
the bracket first so what's in the bracket is 8 out of a hundred plus 1 is
1.08 so we have 1.08 in the bracket to the power of 3 so then when you type it
in it'll just be three thousand times 1.08 to the power of is this button
here to the power of 3 and press equals and you got three seven seven nine point
one four
which i believe is the same answer that we calculated before
so now we're going to do a question where the interest is compounded daily
okay so we always write down the formula first A equals P bracket 1 plus R over a
hundred and bracket NT and then we write P equals R equals n equals T equals P
equals 6500 that's the principal R equals 6 percent per annum T equals 2
years and n is now let's have a look compounded daily and n is the number of
times interest is compounded per year so let me write that down so you don't get
confused number of compounding periods
per year and obviously it'll be 365 because the interest is compounded daily
so there are 365 days in a year so putting all that into our formula we
have 6500 times 1 plus R is 6 over a hundred times 365 notice times 365 is at
the denominator of the fraction times 365
times 2 - so there are a few calculations which I would do first before typing
the calculator the first is where all the times 365s are so there's two of
them so I'm going to do this first so 100 times 365 is 36 thousand five
hundred and then here 365 times 2 730 okay now I
would type this part inside a bracket into the calculator first so it's six
divided by 36500 and then plus 1 which is 1.000164384
and then to the power of 730 now notice how I try not to round this number so put in as
many decimal places as you can so then you have 6,500 times 1.000164384
to the power of 730 so you have seven thousand three hundred and twenty eight point six
six and that is the future value of the investments okay thanks for watching the
tutorial see you next time.